For a given value of diffusion coefficient, there exists a
critical value of \(\Delta _0\)  below which the system gets
extinct, independently of \(\alpha \)  [1]}. Above
this critical value, for every \(\alpha \)  the increase of \(\Delta _0\)  results in the increase of the average number of bugs, but
the pattern formation is not much influenced. The latter is,
however, true solely if \(\Delta _0\)  increases through the
increase of \(r_{b0}\)  and the death rate is low. Namely, as in
the case of global interaction discussed in
Sec. REF , an increase of the death rate, though
accompanied by a compensating increase of birth rate, leads to
larger fluctuations in the particle number. In numerical
simulations we have observed that the larger are the
fluctuations in the number of bugs, the more difficult is the
formation of the periodic pattern, and finally the individuals
do not arrange in the periodic pattern but in random clusters
(see also Ref. [2]}). This effect may in fact make
difficult to observe the periodic clustering phenomenon in real
competitive biological systems.
